Not necessarily, Abe. The grind affects how dark and strong the brewed coffee will be. But the caffine levels are determined by how long the beans were roasted.

With coffee, "strong" is a word describing the flavor. You can, for instance, brew a very strong cup of decaffinated coffee merely by changing the grind.

Do you have access to a coffee press? Normally they are used with a course grind. But try brewing a press using a finer grind (not as fine as esperesso, though, or you'll clog the filter). You should be able to go as fine as a drip grind. Note how much darker and stronger the coffee is, even though you started with the same beans, same amount of water, and steeped them for the same amount of time.

You're asking about brewing methods and not the roast or blend? That is, you're talking about the brewing method of steeping the grinds in an ibrik (aka cezve) as opposed to using an espresso machine to force hot water through a porrofilter pressure-packed with grinds?

Everything else being equal, ounce for ounce, the coffee prepared in an ibrik, according to the usual Greek/ Turkish/ Arab method will be more caffeinated. Offhand, I forget by how much but do recall the difference may primarily be attributed to grind (i.e., contact area), contact time, solubility and temperature variation.

Everything else being equal, cup for cup espresso has about 1/3 less caffeine than found in coffee brewed n "normal" automatic and pour over drip/filter makers. The joker in the deck is that an espresso demitass is about 1/4 the size of a coffee mug. Ounce for ounce, espresso is a little more than twice as caffeinated.

Stupidly, I'm pulling this from that bag of cement I call my head and not from any recent research -- including Wiki. Maybe somebody who's interested should actually research it.

By the way, "espresso roast" coffee is a very poor choice for making espresso. The brewing method so concentrates the flavors that very dark roasts taste horrible. "Espresso" and other extremely dark roasts can work pretty well in fitler-drips though.